I would make an educated guess that the reason why Dropbox hasn't provided this functionality, and likely never will, is because this is a dangerous feature in the hands of unknown developers.

Consider the case where you write an application that uses such a delta-change update system for updating large files. You thoroughly test your app and publish it to an app store. A couple of weeks after your initial release, and numerous downloads, you start receiving bad reviews and complaints because you managed to miss a very specific test case.

Within this specific, buggy case you've miscalculated a differential offset by 1-byte. Oh no! You've now corrupted thousands of files, for hundreds of users!

Considering such a possibility, I think I would personally request that Dropbox NEVER provide such a dev feature. If they integrated such a function into the API, they would be breaking their #1 purpose-- to provide consistent, safe, & reliable cloud backups of your important files.